training manual feflow 7 - mi.fu-berlin.de · prefacei preface 0.1 scope and structure of this...

Training Manual FEFLOW 7.1

Groundwater Modeling with FEFLOW 7.1

August 24, 2017

DHI WASY GmbHGroundwater Modelling Centre

FEFLOW Services

Contents 3

Contents

Preface i0.1 Scope and structure of this manual . . . . . . . . . . . . . . . . . . . . . . i0.2 Exercise data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii0.3 Where to find additional information . . . . . . . . . . . . . . . . . . . . . ii0.4 Trademark legal notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

1 Box - Fluid Flow 11.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Model Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Starting a New Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Supermesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Finite-Element Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.6 Problem Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.7 Model Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.8 Simulation Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.9 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.10 Additional Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Box - Solute Transport 132.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Model Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Problem Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Model Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Simulation Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.6 Oscillation Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Preface i

Preface0.1 Scope and structure of this manual

This training manual serves as a basis for FEFLOW training courses held by DHI instruc-tors.

It is intended to help you to follow the training more easily, to understand the theoreticalbackground of the program and to be able to repeat the examples at home on your own.

It should neither be considered as an alternative FEFLOW Help System nor as a step-by-step tutorial for personal training.

0.1.1 Terms and notations

This manual has been designed to be as self-explanatory as possible. Still, some notationsshould be clarified in advance.

At one side of each page you find some white space to take notes related to the con-tents of the page. The instructor will inform you about helpful details not contained in thismanual, and you will probably wish to write down parts of these explanations.

In the manual, you will basically find four different types of content:

• A detailed description of the steps necessary to complete the examples.

• A basic overview of the theoretical or conceptual background of the steps applied.

• Pointers to the most frequent mistakes.

• References to the other parts of the FEFLOW documentation.

0.1.2 Description of the examples

In addition to verbal descriptions of the required screen actions we make use of someicons. They are intended to assist in relating the written description to the graphical infor-mation provided by FEFLOW. The icons refer to the kind of setting to be done:

menu commandtoolbarpanelbuttoninput box for text or numbersswitch toggleradio buttoncheck boxcontext-menu command

At some points in the text you will find file names printed in color. The respective filesare located on the USB memory stick that comes together with this training manual. Theexact path of these files is given in the introduction to each chapter.

ii Preface

You may use these files as a starting point for your studies later (if you do not want tostart your exercise at the beginning of the chapter again). Please note that DHI WASYdoes not take any responsibility for the correctness and usability of these data.

Other files (e.g., GIS data or background images) are printed in the same color.

0.1.3 Theoretical / conceptual notes

Notes concerning the theoretical background or the basic concepts in FEFLOWcan be found in light blue boxes. They offer a short, practically-oriented overviewof the theory related to the described steps. For more detailed informationplease have a look at the corresponding chapters in the FEFLOW documen-tation.

0.1.4 Pointers to the most frequent mistakes

The most common mistakes are enclosed in light red boxes.

0.1.5 References

References to other parts of the FEFLOW documentation, such as the Help System orarticles of the White Papers are provided in combination with a book sign.

The notation of references is as follows:

WP II 1.3.2

White Papers, Vol. II, Chapter 1.3.2

0.2 Exercise data

Your course material includes a training DVD or a USB memory stick, which contains thistraining manual and the presentation slides as well as the complete FEFLOW documenta-tion (all PDF format).

All data that you need to create the models discussed in this manual can be found in thefolder /model. At the beginning of each exercise, the location of the specific files necessaryfor the section is indicated.

0.3 Where to find additional information

To get further information, please also refer to other parts of the FEFLOW documentation.The following additional documentation material is available:

0.3.1 The FEFLOW documentation

• License Installation Guideline for Windows

• License Installation Guideline for Linux

• Introductory Tutorial

• Help System: The main core of the FEFLOW documentation is provided via theFEFLOW Help System. The help is available locally (requires user installation) andonline. The help gives a detailed description of the user interface. It explains the

Preface iii

essential work steps of model set-up, simulation, post-processing, IFM Programmingand Python Interface.

In each chapter, the respective topic is introduced and the relevant FEFLOW toolsare presented. The underlying concepts and workflows are described, followed by atutorial section.

• White Papers Vol. I - V:

A collection of articles about specific modeling approaches and methods used inFEFLOW.

The entire documentation can be found in PDF format in the /documentation folder ofthe FEFLOW DVD or USB.

0.3.2 The FEFLOW Help system

The Help system provides detailed background information at all stages of modeling. It canbe opened from the FEFLOW menu Help - Help (Online) or Help - Help (Online)(requires previous installation).

0.4 Trademark legal notice

All product names, logos, and brands are property of their respective owners. All company,product and service names used in this training manual are for identification purposes only.Use of these names, logos, and brands does not imply endorsement.

1 Box - Fluid Flow 1

1 Box - Fluid Flow

All files related to this exercise can befound on the training USB memory stickin the project folder /models/box model.

1.1 Objective

By setting up a very simple horizontal 2D model, some basic FEFLOW operations arepracticed.

First, the geometry of the model is defined and a finite-element mesh is generated. Themodel properties - initial, boundary conditions and material properties - are applied.

In a last step, boundary conditions and/or material properties are modified, so that abetter understanding of their effects on the model results can be acquired.

1.2 Model Scenario

The model domain is a simple rectangle with an area of approx. 1000 m x 1000 m. Themain flow direction follows the hydraulic head gradient from the left (western) to the right(eastern) border.

Two production wells exist within the model area. Recharge is applied as a constantvalue all over the model domain. Figure 1.1 illustrates the scenario.

1.3 Starting a New Model

Choose File - New from the menu to start with a new model. The upcoming dialogasks you how the model extents should be specified. Choose Manual input of theinitial domain bounds and click Next.

The horizontal and vertical extent of the model domain is 1000 m. Enter this numberas the maximum value for both the x-Range and the y-Range (the minimum values remainat the default value of 0 m).

Figure 1.1: Model scenario

2 1 Box - Fluid Flow

With a click on Finish, a new model is created and a (Supermesh) view window isopened.

Many features of FEFLOW are organized in Toolbars and Panels. TheView Components panel for example contains a list of elements that can be

displayed in the currently selected view window.Panels and toolbars as well as charts can be arranged in the FEFLOW windowin an arbitrary manner.If a panel, toolbar or chart is not visible, it can be activated from the Viewmenu (Figure 1.2).

Figure 1.2: Activating a panel

1.4 Supermesh

The supermesh defines the geometry of the model.In the simplest case, a supermesh consists of only one polygon that defines theouter boundary. The design of the supermesh also influences the generation ofthe finite-element mesh. More complex supermeshes contain several polygonsand a number of lines and points.

In this simple case, the supermesh consists of one single square polygon with a laterallength of 1000 m as its outer boundary.Click on Add Polygons in the Mesh Editor toolbar.

The polygon is digitized on the display by clicking the left mouse button for each nodeof the supermesh border. The polygon is closed by either double-clicking the left mousebutton or by clicking the first node of the node-string again.

Exact coordinates can be set by pressing the <F2> key on your keyboard instead ofclicking the left mouse button. The result should look like the polygon in Figure 1.3.

box.smh


Figure 1.3: Supermesh

1.5 Finite-Element Mesh

FEFLOW provides the different tools to create a finite-element mesh in the Meshingpanel.

In the Meshing panel click on Supermesh from the panel section From SupermeshElements. This will activate the Properties section for all the Supermesh Elements. Entera number of 500 elements in the Proposed elements field of the Meshing panel.In the upper section of the panel, select Advancing Front from the drop-down list ofgenerators and click on Generate Mesh (Figure 1.4).

Figure 1.4: Meshing panel.

As a result, you should obtain a mesh similar to the one shown in Figure 1.6.

Meshing panel:This contains all the necessary tools to create the finite-element mesh in 2D or3D. The finite-element mesh is the basis of the numerical simulation.In the case of 2D meshing, FEFLOW can work with quadrilateral as well as withtriangular meshes.


Different mesh generators are provided for automatic meshing: Transport Map-ping for quadrilateral; Advancing Front, GridBuilder and Triangle for trian-gles.Advancing Front produces very regular meshes but neglects line and pointfeatures; GridBuilder overcomes this drawback but may fail under certain cir-cumstances. Triangle can handle very complex geometries and is extremelyfast, but yields elements of slightly lower quality.The number of finite-elements can be indicated by the Proposed elements fieldin the Meshing panel, which can be a number either for the entire Supermeshor for a region of the Supermesh.In the case of 3D meshing, FEFLOW works with the TetGen mesh generator,which can produce tetrahedral quality meshes. This type of meshes can beeither created by meshing directly from a 3D Supermesh or by re-meshing anexisting 3D finite-element model.

Figure 1.5: Mesh generators in FEFLOW

boxA1.fem

1.6 Problem Settings

From the main menu choose Edit - Problem Settings.

The Problem Settings dialog is the control center for all general settings of themodel, e.g. the type of the problem (flow only or flow and transport), the tem-poral domain (steady state or transient) or numerical properties like accuracysettings and the choice of the equation solver.


Figure 1.6: The finite-element mesh

The numerous settings of a FEFLOW model are listed in an index on the leftside of the dialog.At the top of the index, you find the Problem Summary, which gives informationon key properties like the Problem Class or the number of nodes and elements.Further down the index, the Problem Class category lets you define the type ofthe model and the respective settings. Other items on the list are the Equation-System Solver, Field-Line Computation settings and Editor Settings.

1.6.1 Problem Class

FEFLOW allows the simulation of flow, groundwater age, mass and heat transport pro-cesses in either saturated or variably saturated media. For both flow and transport simu-lations, a steady-state or a transient solution can be computed.

Saturated/UnsaturatedIn saturated mode, unsaturated parts of the model are either excluded or treatedin a simplified manner. The Darcy equation is used for the entire model domain.In unsaturated mode, Richards’ equation is applied for the unsaturated parts ofthe model.

Flow/TransportFEFLOW can simulate the flow regime exclusively, or in combination with atransport simulation. For transport, you can choose between groundwater age,mass (contaminant) transport, heat transport or any combination of the three.We recommend to always set up a flow model first to check its usability. In asubsequent step, it can be extended to a flow and transport model.

Steady state/TransientIn steady state mode, FEFLOW calculates the state of a model with time-constant


boundary conditions and material properties after an infinitely long time, e.g. tosimulate average conditions for an aquifer. In transient mode, the simulation isdone for a specified time period. This time period is divided into time steps forwhich results are computed (temporal discretization).The steady flow/transient transport mode requires a steady state solution of theflow simulation as initial condition!

Open the Problem Settings dialog via the Edit menu. Choose the Problem Classitem from the index on the left-hand side of the dialog. Switch to Steady for Fluid flow.No further changes are required (see the settings in Figure 1.7).Close the window with OK and confirm the changes with Yes.

Figure 1.7: Defining the problem class in the Problem Settings dialog

boxA2.fem

1.7 Model Properties

The model properties reflect the physical conditions in the model area. This includes initialconditions, boundary conditions and material properties. All model properties can be foundin the Data panel (Figure 1.8).

1.7.1 Initial Conditions

In the Data panel, all model properties are organized in seven major categories (Geom-etry, Process Variables, Boundary Conditions, Material Properties, Auxiliary Data,User Data and Discrete Features).The Process Variables include the primary variables (piezometric head for the flow model,mean age, lifetime expectancy, exit probability, concentration and temperature for transportmodels) and secondary (derived) variables (like Darcy flux, saturation, etc.).The state of the primary variables at the beginning of the simulation reflects the initial con-ditions of the model.With a double-click on Hydraulic head, this property is plotted in the currently active viewwindow. The default initial head is 0 m and will be used for this simple steady-state exam-ple. No changes are necessary.


Figure 1.8: Model properties shown in the Data panel

1.7.2 Boundary Conditions

For the purpose of this exercise, a fixed hydraulic head will be assigned to both the left(30 m) and the right borders (29.85 m).Activate Hydraulic-head BC from the Data panel (Boundary Conditions - Fluid flow )by double-clicking on it. The model turns grey, indicating that no boundary conditions havebeen assigned yet.

By default, all boundaries of a FEFLOW model are impervious.To allow an interaction of the model domain with its environment, boundary con-ditions have to be specified. In FEFLOW, there are five different types of flowboundary conditions: Hydraulic-head BC, Fluid-flux BC, Fluid-transfer BC,Well BC and Multilayer-well BC.

Boundary and initial conditions of a finite-element model are node-based parameters.Before the boundary conditions can be assigned, a selection of nodes must be created asassignment target. In this example, the left border will be selected first.Choose the Select Nodes Along a Border tool from the drop-down list in the Se-lection toolbar.

Move the mouse cursor to the bottom-most node of the left border. Press and hold theleft mouse button. Move the mouse cursor to the topmost node of the left border and


release the mouse button again. You should see that the nodes of the left border are se-lected, indicated by yellow markers as shown in Figure 1.9.

Figure 1.9: Selection of nodes along the left border

In the Editor toolbar, enter a value of 30 m into the input box. Click on As-sign to assign the BC value. The boundary conditions on the left side should now bevisible and highlighted as blue circles.To check the value of the boundary conditions that have just been assigned, activate the

Inspect Nodal/Elemental Values tool in the Inspection toolbar. Move the magni-fying glass over the node that you want to check, and the value of the boundary conditionis displayed in the Inspection panel (Figure 1.10).

Before repeating the same steps for the right model border it is necessary to clear thecurrent selection (otherwise the boundary conditions that have already been set at theactive selection would be overwritten). Go to the Selection toolbar and click on

Clear Selection. Now, repeat the steps for the right border. Choose the SelectNodes Along a Border tool from the Selection toolbar again and select the nodesbetween the bottom-most and the topmost node of the right border.

This time, enter a value of 29.85 m in the input box of the Editor toolbar. Click onAssign to assign the boundary condition. Next, use the Inspect Nodal/Elemental

Values tool a second time to make sure that the values are correct and clear the selectionagain ( Clear Selection).

The last boundary conditions to be set are the two wells. The production wells arelocated within the eastern part of the model, each having a pumping rate of 500 m3/d. Thesteps for assigning well boundary conditions are the same as for the previous boundarycondition: First, select (double-click) Well BC in the Data panel. Second, create aselection that contains two nodes within the right part of the model. An appropriate toolfor creating a selection of single nodes is the Select Individual Mesh Items toolthat can be found in the left drop-down list of the Selection toolbar. Make sure


Figure 1.10: Boundary conditions checked with the Inspect Nodal/Elemental Values tool

that the selection mode Add to Selection is active (second drop-down list in theSelection toolbar). Choose two arbitrary nodes in the right part of the model, and

click on each of them once. Two yellow markers indicate the active selection.

Finally, enter a pumping rate of 500 m3/d in the Editor toolbar and click onAssign.

All required boundary conditions have now been assigned to the model. For a finalcheck, clear the selection by clicking Clear Selection and double-click on BoundaryConditions - Fluid flow in the Data panel to display all types of boundary conditions atthe same time. The result should look similar to Figure 1.11.

For Fluid-flux BC and Well BC type boundary conditions positive values defineoutflow from the model, negative ones define inflow.

boxA3.fem

1.7.3 Material Properties

When a new model is created, FEFLOW assigns default values for all material properties.Except for transmissivity and recharge, these default values will be used for this simpleexample. Double-click on Material Properties - Fluid flow - Transmissivity [max] in the

Data panel.

In a finite-element model, all material properties are elemental values. Both transmis-sivity and recharge are considered as homogeneous. Therefore, a selection containing allelements is to be created for the following data-assignment steps.

Click on Select All in the Selection toolbar (the keyboard shortcut <CTRL +A> has the same effect). Enter a value of 170 in the Editor toolbar and click on

Assign (the FEFLOW default unit is [m2/d]).

One way of representing recharge in a FEFLOW model is using the Source/sink pa-rameter. Double-click on this entry in the Data panel to plot the current distribution inthe active view.


Figure 1.11: All boundary conditions shown in the view window

Type a value of 5e-4 m/d into the input box of the Editor toolbar, click on As-sign again and clear the selection with Clear Selection afterwards.

boxA4.fem

1.8 Simulation Run

To see the changes in the model results while the simulation is being performed, plot thehydraulic-head distribution in the active view by double-clicking on Process Variables -Fluid flow - Hydraulic head in the Data panel. Now, go to the Simulation toolbarand click on Start . After a few seconds, a colored distribution of the resulting hydraulichead is shown in the active view (Figure 1.12).

Figure 1.12: The hydraulic head field as calculated during the model run


1.9 Postprocessing

To study the results in more detail, we use the View Components panel. This panelcontains a list of all properties that are currently displayed in the active view. The compo-nents are sorted in different categories, in this case Geometry and Hydraulic head.

For Hydraulic head, different plot styles are available. The default style is a Continu-ous, interpolated color distribution. To change to a Fringes or Isolines plot style, deacti-vate the check mark in front of Continuous and activate the Fringes or Isolinesstyle instead. Finally, the water balance of the model should be checked. Bring the Rate-Budget panel to the front which is located to the lower right of the FEFLOW interface bydefault. To start the budget calculation, use the Active check box (Figure 1.13).

Figure 1.13: The water balance of the model is shown in the Rate-Budget panel

The Imbalance term in the Rate Budget panel reflects the solver residualerror and the numerical error due to 1) mesh discretization in the case of steady-state problems and 2) both mesh and temporal discretizations in the case oftransient problems. For steady-state problems, the imbalance should be closeto zero.

1.10 Additional Practice

For additional practice of the methods used so far, try to change some parameters, suchas the pumping rates of the wells, the transmissivity, etc., and compare the results.

2 Box - Solute Transport 13

2 Box - Solute Transport

All files related to this exercise can befound on the training USB memory stickin the project folder /models/box model.

2.1 Objective

In this exercise, the 2D flow model is extended to a 2D mass-transport model. Basic con-cepts of mass-transport modeling including boundary conditions and material propertiesare explained.

Common problems in transport modeling, such as oscillations and numerical dispersion,and their prevention strategies are explained and discussed. Boundary constraints areintroduced during the exercise.

2.2 Model Scenario

Two contaminant sources that are located upstream of the wells can potentially affect thewater quality. Therefore, contaminant concentrations at the wells should be determined.For our model, this is done by a steady-state simulation for a worst-case scenario. Thescenario is shown in Figure 2.1.

2.3 Problem Settings

2.3.1 Problem Class

Load the previously created 2D flow model or open boxA4.fem from the training USB stickor DVD. Open the Problem Settings dialog located in the Edit menu.

Choose Problem Class from the index and activate the option Include transport of...Mass (Figure 2.2).To finish, click OK and confirm the changes with Yes.

boxB1.fem

Figure 2.1: Model scenario

14 2 Box - Solute Transport

Figure 2.2: Problem-class settings for steady mass transport

Figure 2.3: Available types of mass-transport boundary conditions

2.4 Model Properties

After the problem class has been changed, additional model properties related to the trans-port model appear in the Data panel. This includes initial and boundary conditions, aswell as material properties.

2.4.1 Initial Conditions

In the Data panel, double click on Process Variables - Mass transport - Mass con-centration.

The state of the process variables at the start of the simulation reflects the initial condi-tions of the model. The default initial condition of 0 mg/l is accepted without changes.

2.4.2 Boundary Conditions

The mass-transport boundary conditions are of a similar type as the flow BCs. Figure 2.3gives an overview of the available boundary-condition types.

The model domain contains two contamination sources. The easiest and probably mostconservative approach - using a fixed concentration - will be used to represent these twosources.


Figure 2.4: Selection for contamination sources

In the Data panel double-click on Boundary Conditions - Mass transport - Mass-concentration BC.

Choose the Select Individual Mesh Items tool from the Selection toolbar.Move the mouse cursor into the view window and select several mesh nodes in the upperleft side of the model with single left-mouse clicks.

Repeat these steps to select a second area in the lower left side of the model. If aselection has been created erroneously, use Clear Selection, Undo LastSelection Step or Redo Last Selection Step buttons of the Selection toolbar.The result should look similar to the selection shown in Figure 2.4.

Finally, enter a value of 100 mg/l into the input field of the Editor toolbar andclick on Assign to set the boundary conditions. The mass-boundary conditions aredisplayed with the same blue symbols that indicate a Hydraulic-head BC.

To check the values of the boundary condition, use the Inspect Nodal/ElementalValues tool again.

Finally, click on Clear Selection to avoid that these boundary conditions are over-written during the following operations. During the next steps, the boundary conditions forthe left and right border are assigned.

At any border with advective inflow, the concentration of the water entering the domainshould be specified. For this model, it is assumed that the inflowing water is freshwaterwith a concentration of 0 mg/l.

Choose the Select Nodes Along a Border tool from the Selection toolbar.Move the mouse cursor to the bottommost node of the left border. Press and hold the leftmouse button. Move the mouse cursor to the topmost node of the left border and releasethe mouse button again. You should see that the nodes of the left border are selected,indicated by yellow markers.

Repeat these steps for the right border. The nodes of the left and the right border arehighlighted in yellow. Go to the Editor toolbar and enter a value of 0 mg/l into theinput field. Click on Assign to assign the values. The boundary conditions on the leftand right side should now be visible as blue circles (Figure 2.5).

To check the values of the boundary condition, activate the Inspect Nodal/ElementalValues again. Move the magnifying glass over the nodes to check the assigned value of


Figure 2.5: Nodal selection and mass boundary condition

the boundary condition.

boxB2.fem

Constraints

The flow-boundary conditions assigned to the model (Hydraulic-head BC at left and rightborder) potentially allow for both in- and outflow.

In a transport simulation, borders with an inward-flow direction have to be treated in adifferent way than borders with an outward-flow direction. In the former case, the con-centration at the border should be fixed, while in the latter case, free advective outflow isrequired, and the mass-boundary condition therefore has to be deactivated. This can beachieved by a second, complementary condition that is called a Constraint in FEFLOW.

Constraints limit the application of boundary conditions.A good example is a well with a constant pumping rate, whose drawdown shouldbe limited to a certain level (Figure 2.6). The minimum hydraulic head to whichdewatering is allowed is defined as a constraint. If the hydraulic head at thewell node is above the minimum head, the well-boundary condition is applied.If the hydraulic head would drop below the minimum head, the well-boundarycondition is internally turned into a head-boundary condition with the value ofthe minimum head.Please note that when using the settings mentioned above for a well-boundarycondition limited by a minimum head, it is possible that the groundwater leveldrops below the minimum head due to effects in the surroundings of the well.In that specific case, the well will be turned - most likely unwanted - into ahead-boundary condition which will lead to an infiltration of water instead ofa reduction of the pumping rate. To avoid this, a well can be set up with a differ-ent boundary condition/constraint combination: Use a head-boundary conditionwith a value of the minimum head and limit the outflow using a minimum flow-rate constraint with a value of the pumping rate of the well. To avoid any inflow,use a maximum flow-rate constraint of 0 at the same time.


Figure 2.6: A pumping well with limited screen depth as an application example for con-straints

Figure 2.7: Comparison of the sign convention for budget results, constraints and bound-ary conditions

Note: Unlike the definition for boundary conditions, for constraint conditions offlux type, positive values define an inflow into the model, negative ones an out-flow (Figure 2.7).

By default, constraints are not shown as a parameter in the Data panel and have tobe made visible first. Use the right mouse button to open the context menu of the itemBoundary Conditions - Mass transport - Mass-concentration BC in the Data panel.Choose Add Parameter - Min. mass-flow constraint .

Double-click on the new parameter to activate it for assignment (Figure 2.8). Go to theEditor toolbar and enter a value of 0 g/d into the input field. Finish the assignment

with a click on Assign.

The constraints are now indicated in the view window by horizontal bars below theboundary-condition symbols.

As a last step, click on Clear Selection in the Selection toolbar.

When using constraints, it is recommended to use a transient model approach.The reason for doing so is the fact that the check whether the boundary conditionor the constraint should be active is done at every time step for a transient run.In a steady-state model, this check is only done for the first iteration and thenkept for the subsequent iterations.

boxB3.fem


Figure 2.8: Data panel showing the minimum mass-flow constraint

2.4.3 Material Properties

For the simulation of a mass-transport problem, additional material properties are avail-able, including sorption isotherms and reaction terms.

For the sake of simplicity, default parameters are used for this model. Please note: Forpractical applications, you should at least adapt porosity and dispersivity values to localconditions. The default values are 30 % for porosity, 5 m for the longitudinal and 0.5 m forthe transverse dispersivity.

Three different mechanisms need to be considered for contaminant transportwithin a porous medium:

• Advection,

• Molecular diffusion and

• Dispersion.

Dispersion occurs due to differences in transport velocities caused by matrixvariations (microdispersivity, Figure 2.9) and by geological inhomogeneities oflarger spatial scales (macrodispersivity).Dispersion is usually considered by applying the linear Bear-Scheidegger dis-persivity law, which distinguishes between a dispersivity parameter in flow direc-tion (longitudinal dispersivity) and a dispersivity parameter perpendicular to theflow direction (transverse dispersivity). The longitudinal dispersivity depends onthe length scale of the phenomenon. Figure 2.10 shows a chart of measuredlongitudinal dispersivities in relation to the spatial scale.In comparison to longitudinal dispersivity, much less is known about transversedispersivity, and often, the ratio at/al of transverse over longitudinal dispersivi-ties is assumed to be 0.1. However, even that factor varies widely in laboratoryand field experiments.


Figure 2.9: Comparison of purely advective and real mass transport (taken from: [?])

Figure 2.10: Longitudinal dispersivity vs. scale of phenomenon (taken from: [?])


Figure 2.11: Result of mass-transport simulation (coarse mesh)

2.5 Simulation Run

Plot the initial concentration in the active view by double-clicking on Process Variables -Mass transport - Mass concentration in the Data panel.

To start the simulation run, click on Start in the Simulation toolbar. After ashort time, the result is shown. To turn the display of element edges off in the current view,use the check mark in front of Geometry - Edges in the View Components panel.

As Figure 2.11 shows, the current model setup results in negative concentrations. Thisis a clear indication for model instability; the reason for this being an insufficiently finespatial discretization.

To improve the model result, the mesh has to be refined.Before any further changes can be done, the simulation must be stopped by clicking onStop in the Simulation toolbar.

Create a selection of all nodes using Select All in the Selection toolbar (orpress <Ctrl + A> on your keyboard). Click on Refine Elements in the MeshGeometry toolbar twice to refine the mesh.

Clear Selection and run the simulation again.The two contamination plumes should now be visible in the resulting concentration field.

When checking the results in more detail, one finds that negative results still occur at thefronts of the contaminant plume. Figure 2.12 shows a close-up of the contamination source(the element edges have been reactivated for this figure). Upstream of the contaminantsources, high and low concentrations change at regular intervals.

This is a typical oscillation pattern in transport models.

Oscillations in a transport simulation can occur if the discretization is insufficient,i.e., if the mesh is too coarse or if time steps are too large. There are three majorstrategies to reduce oscillations:

• Mesh refinement

• Upwind techniques


Figure 2.12: Concentration distribution near the contamination sources

• Increasing dispersivity values

The first approach always is the preferable solution as mesh refinement doesnot change the physical properties of the model. However, in some cases, meshrefinement might not be an option due to restrictions in memory and/or compu-tation time.

Upwind techniques add numerical dispersion to the model, the most generalone - full upwinding - in all directions, the most restricted one - shock capturing- only where it is necessary. Upwind techniques always change the dispersivityapplied to a model, and therefore lead to a larger contaminant plume.

Increasing the dispersivity also leads to a more stable simulation as gradientsin concentration or temperature are reduced. However, increasing dispersivityvalues artificially changes the physical properties of the system.

2.6 Oscillation Prevention

As the oscillations in the model are too high, all of the following solution approaches shouldbe tried in order to reduce the oscillations.

2.6.1 Mesh Refinement

Repeat the steps described in section 2.5 to refine the mesh several times. As a result, theoscillations become smaller and the shape of the concentration plume can be reproduced.Additionally, concentration over- and undershoots are gradually reduced or removed com-pletely. In further steps, it is possible to refine the mesh locally by selecting the nodesaround the contamination sources using the Select in Rectangular Region tool. Theselection and the result are shown in Figures 2.13 and 2.14.

For transport simulations, the Peclet criterion can be useful for determining therequired mesh density. The Peclet Number is available as elemental distribu-tion in Auxiliary Data in the Spatial Units panel. The dimensionless Peclet


Number relates the Darcy velocity, characteristic length of the finite element anddispersivity values.

Figure 2.13: Local refinement for mass-transport simulation

Figure 2.14: Result of mass-transport simulation (fine mesh with approx. 10,000 elements)

boxB3a.fem

2.6.2 Upwinding

To activate an upwinding technique, open the Problem Settings dialog via the Editmenu.

Here, open Problem Class - Numerical Parameters. Choose Full upwinding.Press OK and confirm the changes with Yes.


Run the simulation again. In the best case, there will be no negative values in theresulting concentration field. However, it can be seen that the sharp fronts of the plumeare artificially smoothed as a result of the extra numerical dispersion (Figure 2.15).

Figure 2.15: Result of mass-transport simulation with Full Upwinding

boxB3b.fem

2.6.3 Increasing Dispersivity Values

Reload the model BoxB3a.fem via File - Open. In the Data panel, double-click onMaterial Properties - Mass transport - Longitudinal dispersivity and create a selectionof all elements by clicking on Select All in the Selection toolbar (or press<Ctrl+A> on your keyboard). Enter a value of 50 m into the input field of the Editortoolbar and click on Assign.

Repeat these steps for the Transverse dispersivity and assign a value of 5 m.After running the simulation again, the result looks similar to the one of the simulation

with full upwinding but the spreading of the contaminant plume in both longitudinal andtransverse flow direction is even larger(Figure 2.16).

boxB3c.fem


Figure 2.16: Result of mass-transport simulation with increased dispersivity values

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